Package

scala

math

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package math

The package object scala.math contains methods for performing basic numeric operations such as elementary exponential, logarithmic, root and trigonometric functions.

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package.scala
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Type Members

  1. final class BigDecimal extends ScalaNumber with ScalaNumericConversions with Serializable

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    BigDecimal represents decimal floating-point numbers of arbitrary precision.

    BigDecimal represents decimal floating-point numbers of arbitrary precision. By default, the precision approximately matches that of IEEE 128-bit floating point numbers (34 decimal digits, HALF_EVEN rounding mode). Within the range of IEEE binary128 numbers, BigDecimal will agree with BigInt for both equality and hash codes (and will agree with primitive types as well). Beyond that range--numbers with more than 4934 digits when written out in full--the hashCode of BigInt and BigDecimal is allowed to diverge due to difficulty in efficiently computing both the decimal representation in BigDecimal and the binary representation in BigInt.

    When creating a BigDecimal from a Double or Float, care must be taken as the binary fraction representation of Double and Float does not easily convert into a decimal representation. Three explicit schemes are available for conversion. BigDecimal.decimal will convert the floating-point number to a decimal text representation, and build a BigDecimal based on that. BigDecimal.binary will expand the binary fraction to the requested or default precision. BigDecimal.exact will expand the binary fraction to the full number of digits, thus producing the exact decimal value corresponding to the binary fraction of that floating-point number. BigDecimal equality matches the decimal expansion of Double: BigDecimal.decimal(0.1) == 0.1. Note that since 0.1f != 0.1, the same is not true for Float. Instead, 0.1f == BigDecimal.decimal((0.1f).toDouble).

    To test whether a BigDecimal number can be converted to a Double or Float and then back without loss of information by using one of these methods, test with isDecimalDouble, isBinaryDouble, or isExactDouble or the corresponding Float versions. Note that BigInt's isValidDouble will agree with isExactDouble, not the isDecimalDouble used by default.

    BigDecimal uses the decimal representation of binary floating-point numbers to determine equality and hash codes. This yields different answers than conversion between Long and Double values, where the exact form is used. As always, since floating-point is a lossy representation, it is advisable to take care when assuming identity will be maintained across multiple conversions.

    BigDecimal maintains a MathContext that determines the rounding that is applied to certain calculations. In most cases, the value of the BigDecimal is also rounded to the precision specified by the MathContext. To create a BigDecimal with a different precision than its MathContext, use new BigDecimal(new java.math.BigDecimal(...), mc). Rounding will be applied on those mathematical operations that can dramatically change the number of digits in a full representation, namely multiplication, division, and powers. The left-hand argument's MathContext always determines the degree of rounding, if any, and is the one propagated through arithmetic operations that do not apply rounding themselves.

    Version

    1.1

  2. final class BigInt extends ScalaNumber with ScalaNumericConversions with Serializable

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    Version

    1.0, 15/07/2003

  3. trait Equiv[T] extends Serializable

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    A trait for representing equivalence relations.

    A trait for representing equivalence relations. It is important to distinguish between a type that can be compared for equality or equivalence and a representation of equivalence on some type. This trait is for representing the latter.

    An equivalence relation is a binary relation on a type. This relation is exposed as the equiv method of the Equiv trait. The relation must be:

    1. reflexive: equiv(x, x) == true for any x of type T.
    2. symmetric: equiv(x, y) == equiv(y, x) for any x and y of type T.
    3. transitive: if equiv(x, y) == true and equiv(y, z) == true, then equiv(x, z) == true for any x, y, and z of type T.
    Version

    1.0, 2008-04-03

    Since

    2.7

  4. trait Fractional[T] extends Numeric[T]

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    Since

    2.8

  5. trait Integral[T] extends Numeric[T]

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    Since

    2.8

  6. trait LowPriorityEquiv extends AnyRef

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  7. trait LowPriorityOrderingImplicits extends AnyRef

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  8. trait Numeric[T] extends Ordering[T]

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  9. trait Ordered[A] extends Comparable[A]

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    A trait for data that have a single, natural ordering.

    A trait for data that have a single, natural ordering. See scala.math.Ordering before using this trait for more information about whether to use scala.math.Ordering instead.

    Classes that implement this trait can be sorted with scala.util.Sorting and can be compared with standard comparison operators (e.g. > and <).

    Ordered should be used for data with a single, natural ordering (like integers) while Ordering allows for multiple ordering implementations. An Ordering instance will be implicitly created if necessary.

    scala.math.Ordering is an alternative to this trait that allows multiple orderings to be defined for the same type.

    scala.math.PartiallyOrdered is an alternative to this trait for partially ordered data.

    For example, create a simple class that implements Ordered and then sort it with scala.util.Sorting:

    case class OrderedClass(n:Int) extends Ordered[OrderedClass] {
    	def compare(that: OrderedClass) =  this.n - that.n
    }
    
    val x = Array(OrderedClass(1), OrderedClass(5), OrderedClass(3))
    scala.util.Sorting.quickSort(x)
    x

    It is important that the equals method for an instance of Ordered[A] be consistent with the compare method. However, due to limitations inherent in the type erasure semantics, there is no reasonable way to provide a default implementation of equality for instances of Ordered[A]. Therefore, if you need to be able to use equality on an instance of Ordered[A] you must provide it yourself either when inheriting or instantiating.

    It is important that the hashCode method for an instance of Ordered[A] be consistent with the compare method. However, it is not possible to provide a sensible default implementation. Therefore, if you need to be able compute the hash of an instance of Ordered[A] you must provide it yourself either when inheriting or instantiating.

    Version

    1.1, 2006-07-24

    See also

    scala.math.Ordering, scala.math.PartiallyOrdered

  10. trait Ordering[T] extends Comparator[T] with PartialOrdering[T] with Serializable

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    Ordering is a trait whose instances each represent a strategy for sorting instances of a type.

    Ordering is a trait whose instances each represent a strategy for sorting instances of a type.

    Ordering's companion object defines many implicit objects to deal with subtypes of AnyVal (e.g. Int, Double), String, and others.

    To sort instances by one or more member variables, you can take advantage of these built-in orderings using Ordering.by and Ordering.on:

    import scala.util.Sorting
    val pairs = Array(("a", 5, 2), ("c", 3, 1), ("b", 1, 3))
    
    // sort by 2nd element
    Sorting.quickSort(pairs)(Ordering.by[(String, Int, Int), Int](_._2))
    
    // sort by the 3rd element, then 1st
    Sorting.quickSort(pairs)(Ordering[(Int, String)].on(x => (x._3, x._1)))

    An Ordering[T] is implemented by specifying compare(a:T, b:T), which decides how to order two instances a and b. Instances of Ordering[T] can be used by things like scala.util.Sorting to sort collections like Array[T].

    For example:

    import scala.util.Sorting
    
    case class Person(name:String, age:Int)
    val people = Array(Person("bob", 30), Person("ann", 32), Person("carl", 19))
    
    // sort by age
    object AgeOrdering extends Ordering[Person] {
      def compare(a:Person, b:Person) = a.age compare b.age
    }
    Sorting.quickSort(people)(AgeOrdering)

    This trait and scala.math.Ordered both provide this same functionality, but in different ways. A type T can be given a single way to order itself by extending Ordered. Using Ordering, this same type may be sorted in many other ways. Ordered and Ordering both provide implicits allowing them to be used interchangeably.

    You can import scala.math.Ordering.Implicits to gain access to other implicit orderings.

    Annotations
    @implicitNotFound( msg = ... )
    Version

    0.9.5, 2008-04-15

    Since

    2.7

    See also

    scala.math.Ordered, scala.util.Sorting

  11. trait PartialOrdering[T] extends Equiv[T]

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    A trait for representing partial orderings.

    A trait for representing partial orderings. It is important to distinguish between a type that has a partial order and a representation of partial ordering on some type. This trait is for representing the latter.

    A partial ordering is a binary relation on a type T, exposed as the lteq method of this trait. This relation must be:

    • reflexive: lteq(x, x) == true, for any x of type T.
    • anti-symmetric: if lteq(x, y) == true and lteq(y, x) == true then equiv(x, y) == true, for any x and y of type T.
    • transitive: if lteq(x, y) == true and lteq(y, z) == true then lteq(x, z) == true, for any x, y, and z of type T.

    Additionally, a partial ordering induces an equivalence relation on a type T: x and y of type T are equivalent if and only if lteq(x, y) && lteq(y, x) == true. This equivalence relation is exposed as the equiv method, inherited from the Equiv trait.

    Version

    1.0, 2008-04-0-3

    Since

    2.7

  12. trait PartiallyOrdered[+A] extends AnyRef

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    A class for partially ordered data.

    A class for partially ordered data.

    Version

    1.0, 23/04/2004

  13. trait ScalaNumericAnyConversions extends Any

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    Conversions which present a consistent conversion interface across all the numeric types, suitable for use in value classes.

  14. trait ScalaNumericConversions extends ScalaNumber with ScalaNumericAnyConversions

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    A slightly more specific conversion trait for classes which extend ScalaNumber (which excludes value classes.)

Value Members

  1. object BigDecimal extends Serializable

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    Version

    1.1

    Since

    2.7

  2. object BigInt extends Serializable

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    Version

    1.0, 15/07/2003

    Since

    2.1

  3. final val E: Double(2.718281828459045)

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    The double value that is closer than any other to e, the base of the natural logarithms.

  4. object Equiv extends LowPriorityEquiv with Serializable

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  5. object Fractional extends Serializable

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  6. def IEEEremainder(x: Double, y: Double): Double

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  7. object Integral extends Serializable

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  8. object Numeric extends Serializable

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    Since

    2.8

  9. object Ordered

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  10. object Ordering extends LowPriorityOrderingImplicits with Serializable

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    This is the companion object for the scala.math.Ordering trait.

    This is the companion object for the scala.math.Ordering trait.

    It contains many implicit orderings as well as well as methods to construct new orderings.

  11. final val Pi: Double(3.141592653589793)

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    The double value that is closer than any other to pi, the ratio of the circumference of a circle to its diameter.

  12. def abs(x: Double): Double

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  13. def abs(x: Float): Float

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  14. def abs(x: Long): Long

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  15. def abs(x: Int): Int

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  16. def acos(x: Double): Double

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  17. def asin(x: Double): Double

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  18. def atan(x: Double): Double

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  19. def atan2(y: Double, x: Double): Double

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    Converts rectangular coordinates (x, y) to polar (r, theta).

    Converts rectangular coordinates (x, y) to polar (r, theta).

    y

    the abscissa coordinate

    x

    the ordinate coordinate

    returns

    the theta component of the point (r, theta) in polar coordinates that corresponds to the point (x, y) in Cartesian coordinates.

  20. def cbrt(x: Double): Double

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    Returns the cube root of the given Double value.

  21. def ceil(x: Double): Double

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  22. def cos(x: Double): Double

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  23. def cosh(x: Double): Double

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    Returns the hyperbolic cosine of the given Double value.

  24. def exp(x: Double): Double

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    Returns Euler's number e raised to the power of a double value.

    Returns Euler's number e raised to the power of a double value.

    x

    the exponent to raise e to.

    returns

    the value ea, where e is the base of the natural logarithms.

  25. def expm1(x: Double): Double

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    Returns exp(x) - 1.

  26. def floor(x: Double): Double

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  27. def hypot(x: Double, y: Double): Double

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    Returns the square root of the sum of the squares of both given Double values without intermediate underflow or overflow.

  28. def log(x: Double): Double

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    Returns the natural logarithm of a double value.

    Returns the natural logarithm of a double value.

    x

    the number to take the natural logarithm of

    returns

    the value logₑ(x) where e is Eulers number

  29. def log10(x: Double): Double

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    Returns the base 10 logarithm of the given Double value.

  30. def log1p(x: Double): Double

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    Returns the natural logarithm of the sum of the given Double value and 1.

  31. def max(x: Double, y: Double): Double

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  32. def max(x: Float, y: Float): Float

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  33. def max(x: Long, y: Long): Long

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  34. def max(x: Int, y: Int): Int

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  35. def min(x: Double, y: Double): Double

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  36. def min(x: Float, y: Float): Float

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  37. def min(x: Long, y: Long): Long

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  38. def min(x: Int, y: Int): Int

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  39. def pow(x: Double, y: Double): Double

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    Returns the value of the first argument raised to the power of the second argument.

    Returns the value of the first argument raised to the power of the second argument.

    x

    the base.

    y

    the exponent.

    returns

    the value xy.

  40. def random: Double

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    Returns a double value with a positive sign, greater than or equal to 0.0 and less than 1.0.

  41. def rint(x: Double): Double

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    Returns the double value that is closest in value to the argument and is equal to a mathematical integer.

    Returns the double value that is closest in value to the argument and is equal to a mathematical integer.

    x

    a double value

    returns

    the closest floating-point value to a that is equal to a mathematical integer.

  42. def round(x: Double): Long

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    Returns the closest Long to the argument.

    Returns the closest Long to the argument.

    x

    a floating-point value to be rounded to a Long.

    returns

    the value of the argument rounded to the nearestlong value.

  43. def round(x: Float): Int

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    Returns the closest Int to the argument.

    Returns the closest Int to the argument.

    x

    a floating-point value to be rounded to a Int.

    returns

    the value of the argument rounded to the nearest Int value.

  44. def signum(x: Double): Double

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  45. def signum(x: Float): Float

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  46. def signum(x: Long): Long

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  47. def signum(x: Int): Int

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    Note that these are not pure forwarders to the java versions.

    Note that these are not pure forwarders to the java versions. In particular, the return type of java.lang.Long.signum is Int, but here it is widened to Long so that each overloaded variant will return the same numeric type it is passed.

  48. def sin(x: Double): Double

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  49. def sinh(x: Double): Double

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    Returns the hyperbolic sine of the given Double value.

  50. def sqrt(x: Double): Double

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    Returns the square root of a double value.

    Returns the square root of a double value.

    x

    the number to take the square root of

    returns

    the value √x

  51. def tan(x: Double): Double

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  52. def tanh(x: Double): Double

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    Returns the hyperbolic tangent of the given Double value.

  53. def toDegrees(x: Double): Double

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    Converts an angle measured in radians to an approximately equivalent angle measured in degrees.

    Converts an angle measured in radians to an approximately equivalent angle measured in degrees.

    x

    angle, in radians

    returns

    the measurement of the angle x in degrees.

  54. def toRadians(x: Double): Double

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    Converts an angle measured in degrees to an approximately equivalent angle measured in radians.

    Converts an angle measured in degrees to an approximately equivalent angle measured in radians.

    x

    an angle, in degrees

    returns

    the measurement of the angle x in radians.

  55. def ulp(x: Float): Float

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    Returns the size of an ulp of the given Float value.

  56. def ulp(x: Double): Double

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    Returns the size of an ulp of the given Double value.

Deprecated Value Members

  1. def round(x: Long): Long

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    There is no reason to round a Long, but this method prevents unintended conversion to Float followed by rounding to Int.

    There is no reason to round a Long, but this method prevents unintended conversion to Float followed by rounding to Int.

    Annotations
    @deprecated
    Deprecated

    (Since version 2.11.0) This is an integer type; there is no reason to round it. Perhaps you meant to call this with a floating-point value?

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